Fields of Experts are high-order Markov random field (MRF) models with potential functions that extend over large pixel neighborhoods. The clique potentials are modeled as a Product of Experts using nonlinear functions of many linear filter responses. In contrast to previous MRF approaches, all parameters, including the linear filters themselves, are learned from training data. A Field of Experts (FoE) provides a generic, expressive image prior that can capture the statistics of natural scenes, and can be used for a variety of machine vision tasks. The capabilities of FoEs are demonstrated with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the FoE model is trained on a generic image database and is not tuned toward a specific application, the results compete with specialized techniques.

This chapter introduces the concept of a Steerable Random Field (SRF). In contrast to traditional Markov random field (MRF) models in low-level vision, the random field potentials of a SRF are defined in terms of filter responses that are steered to the local image structure. This steering uses the structure tensor to obtain derivative responses that are either aligned with, or orthogonal to, the predominant local image structure. Analysis of the statistics of these steered filter responses in natural images leads to the model proposed here. Clique potentials are defined over steered filter responses using a Gaussian scale mixture model and are learned from training data. The SRF model connects random fields with anisotropic regularization and provides a statistical motivation for the latter. Steering the random field to the local image structure improves image denoising and inpainting performance compared with traditional pairwise MRFs.

1999

One of the effects of the PARC Artist In Residence (PAIR) program has been to expose the strong connections between scientists and artists. Both do what they do because they need to do it. They are often called upon to justify their work in order to be allowed to continue to do it. They need to justify it to funders, to sponsoring institutions, corporations, the government, the public. They publish papers, teach workshops, and write grants touting the educational or health benefits of what they do. All of these things are to some extent valid, but the fact of the matter is: artists and scientists do their work because they are driven to do it. They need to explore and create.
This chapter attempts to give a flavor of one multi-way "PAIRing" between performance artist PamelaZ and two PARC researchers, Michael Black and David Levy. The three of us paired up because we found each other interesting. We chose each other. While most artists in the program are paired with a single researcher Pamela jokingly calls herself a bigamist for choosing two PAIR "husbands" with different backgrounds and interests.
There are no "rules" to the PAIR program; no one told us what to do with our time. Despite this we all had a sense that we needed to produce something tangible during Pamela's year-long residency. In fact, Pamela kept extending her residency because she did not feel as though we had actually made anything concrete. The interesting thing was that all along we were having great conversations, some of which Pamela recorded. What we did not see at the time was that it was these conversations between artists and scientists that are at the heart of the PAIR program and that these conversations were changing the way we thought about our own work and the relationships between science and art.
To give these conversations their due, and to allow the reader into our PAIR interactions, we include two of our many conversations in this chapter.

1999

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems